Where did Yosef permit them to do business in Egypt?
Ramban #1, Malbim: Shinu (they lied to their father) mi'Pnei ha'Shalom, to encourage him to fulfill their request of sending Binyamin down to Egypt with them.
Ramban #2: He did indeed grant them permission, even though the Torah did not record it there. 1
Ramban: Just as they told Yaakov that "Sha'ol Sha'ul Lanu ha'Ish... " and "Kulanu Bnei Ish Echad Nachnu;" and again later, when Yehudah said to Yosef, "Adoni Sha'al Es Avadav Leimor ha'Yesh Lachem Av O Ach?" (Bereishis 42:19), even though we do not find Yosef having said that (See Ramban). Refer also to 42:21:2:3.
What is the meaning of "Tischaru"?
Rashi: "Tischaru" is a borrowed term (from the word Socher - businessman) which means that they would be free to move around Egypt (and to buy grain unmolested if they would substantiate their words).
Ramban: They will be free to bring whatever they wished to pay for grain, but he would not accept it from them - to compensate the embarrassment that they had suffered.
Oznayim la'Torah: According to the rules that Yosef had initiated, nobody else was allowed to sell grain. Moreover, had the brothers returned immediately with Binyamin, they would not have been entitled to purchase grain until they had finished what they bought the first time. Only, in order to encourage them to bring Binyamin, he had waived these rules and promised them that they would be able to purchase grain immediately and even to sell what they received.
Why did he say two matters - "Ki Lo Meraglim Atem, Ki Kenim Atem"?
Ha'amek Davar: If I find that you are not spies, but you do not have a base (families), I will return your brother, but you may not do business. 1 Who knows what will come from such people?! If you have a base, you may also do business.
I do not understand his source to say so. The verse says both conditions (you are not spies, and you have a base) followed by both consequences (I will return your brother, and you may do business! - PF)